Either via automatic installation using the above .pet software package

Or, via manual installation:

Download J.R.E. from www.java.com. Select the “Linux (self-extracting file)” not the one with RPM in the name.
When the file is downloaded open a Rox-filer window and go to the place where you downloaded Java. Right-click on the file and select Permissions and Yes to make the file executable. Right-click and select Window > Terminal Here, and enter

./jre-6uXX-linux-i586.bin

Do not forget the "./" to begin (that is period – forward slash, to indicate that the file is found in the current directory). You will need to scroll down with the Enter key to accept the license agreement and then the install program will create a folder named something like jre-1.6.0_XX.